%AMcEneaney, William%ADower, Peter%D2020%I
%K
%MOSTI ID: 10170566
%PMedium: X
%TA min-plus fundamental solution semigroup for a class of approximate infinite dimensional optimal control problems
%XBy exploiting min-plus linearity, semiconcavity,
and semigroup properties of dynamic programming, a fundamental
solution semigroup for a class of approximate finite
horizon linear infinite dimensional optimal control problems is
constructed. Elements of this fundamental solution semigroup
are parameterized by the time horizon, and can be used to
approximate the solution of the corresponding finite horizon
optimal control problem for any terminal cost. They can also
be composed to compute approximations on longer horizons.
The value function approximation provided takes the form of
a min-plus convolution of a kernel with the terminal cost. A
general construction for this kernel is provided, along with a
spectral representation for a restricted class of sub-problems.